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Speaking Mathanese: More About the Dividend Yield

Welcome back to another edition of "Speaking Mathanese," our Motley Fool series that tackles financial math myths and deconstructs the computations that make the biggest difference to your bottom line.

This week, our quest to make you smarter than a fifth-grader takes us back to the delightful den of the dividend yield for the math you need to know to get filthy rich.

The myth
First, the question behind this week's lesson:

If dividend yield is calculated on current price and current dividend ... what is the actual dividend calculation for a stock that has been owned for a period of years and bought at a significantly reduced price?

Talk about a great question. Research says that dividends from blue-chippers like Altria (NYSE: MO  ) , General Electric (NYSE: GE  ) , Procter & Gamble (NYSE: PG  ) , and Johnson & Johnson (NYSE: JNJ  ) accounted for 97% of the stock market's total return from 1871 to 2003.

How, you ask? Through reinvesting. I know, that sounds like poker. "Rats. Busted out on Sirius Satellite Radio again. Time to reinvest."

The math
Fortunately, that's not the way the game works. Reinvesting is one of the few really great things good brokers can do for your portfolio.

Let's say you own 100 shares of Acme Rockets (Ticker: BOOM), which pays a $0.25 dividend per quarter. For you, this means a $25.00 quarterly payout. Your broker will take that cash, usually free of charge, and buy more shares of Acme on your behalf.

Since Acme trades for $50.00 per share, you've just purchased 0.50 shares. You own 100.50 shares, and you'll get paid according to that new share count next quarter. So if the dividend remains $0.25 a stub, you'll receive $25.13.

And more the next quarter. And more the quarter after that. And more the quarter after that. And so on and so on and so on.

So, how does this compounding affect your effective yield? Here's the math:

Total dividends paid / cost basis

Let's say, like this guy, you were investing for 47 years. And in that time, you accumulated an additional 100 shares of Acme through reinvesting. (You now own 200 shares total.) Now let's say that the stock still pays $1.00 per share per year in dividends. You're receiving $200 annually for your $5,000 initial investment (100 shares at $50 apiece). Your effective yield is 4.00% ($200 / $5,000 = 0.04, or 4.00%).

Questions? Submit them here. Otherwise, I'll see you next week, when we dig into the mathanese of total stock return.

For more money ideas, get 30 days of free access to Motley Fool Green Light  right now. There's no obligation to subscribe.

Johnson & Johnson is an Income Investor pick.

Fool contributor Tim Beyers writes weekly about personal finance and investing basics. Have a Foolish money tip? Tell him. Tim didn't own shares in any of the companies mentioned in this article at the time of publication. Tim's portfolio holdings can be found at his Fool profile. His thoughts on personal finance, Foolishness, and investing in general may be found in his blog. The Motley Fool's disclosure policy is lobbying its local school district for a course in beginning mathanese.

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